I was reading through my Analysis notes on Wednesday. I was hoping through most of them (~120 pages total)… but I seriously underestimated the amount of thinking required to read them. Anyway, right on page 4, I encountered a single sentence that stopped me dead and got me thinking for about an hour straight: Do [...]

I saw this interesting problem on The Daily WTF the other day: Josephus and forty of his fellow soldiers retreated from the siege of Yodfat to a small cave in the hills. Surrounded by the Roman legion with no chance of escape, the soldiers saw no other choice but to commit suicide. Like the people [...]

I heard our professor Dales say a cool thing in one of the lectures a few months back, and I only got around to writing it down now. The question is simple: What does… … tend to as n tends to infinity? Here are two arguments: 1. The inside of the bracket goes to 1 [...]

I recently came across this really interesting puzzle: Three players enter a room and a red or blue hat is placed on each person’s head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other [...]

Ok, this is an eighteenth century problem first proposed by Georges-Louis Leclerc, Comte de Buffon (Yes that is only one name!). Suppose a 2 inch needle is randomly thrown or dropped onto a floor made up of wooden boards which are also 2 inches wide and are placed side by side. Now the question is what [...]

A cool thing I learned a long time ago is that 0.99999… = 1. And I mean exactly equal. Not just “very close to”. EXACTLY equal. Behold the proof! Let a = 0.111111… Then 10a = 1.11111… 10a – a = 1.11111… – 0.11111… 9a = 1. But 9 times 0.11111… is 0.99999…. So 0.999999…. [...]

Some years ago, when I first learned about imaginary numbers, I asked myself the inevitable question – “What’s the square root of i?” Okay, so i is the square root of -1. I had come to grips with that concept. But after that, when you start thinking about it… surely the square root of i [...]

The Mathematics of Oz: Mental Gymnastics form Beyond the Edge This is a math puzzle book, and quite a nice short sci-fi story as well. It follows good ol’ Dorothy , as an alien (Oz) captures her, her faithful companion Toto and the entirety of Kansas to perform odd experiments. Particularly mathematical experiments on Dorothy [...]

Hey, let’s play a game! I’ve got 4 dice here. We both pick a die, and then roll to see who gets the higher number. And since you’re my guest, I’ll let you pick your die first, and then I’ll pick mine. Sounds good? Oh, I almost forgot to mention. My dice are numbered a [...]

We math geeks like to play. And one thing we like to play with a lot are series. A series is an infinite row of numbers following a certain rule, all added up. Let me show you two examples: S1 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + [...]